Five different teams could have multiple first round picks in the 2016 NBA Draft this June. I do not expect all of those teams to utilize all of those picks on draft night. Many teams lack the necessary roster space to include that many rookies on guaranteed contracts (although stashing European prospects is an option in an internationally heavy draft) or are built in a way that likely precludes them from desiring that many young players on the roster at once. Then there are the New Orleans Pelicans.
Anthony Davis has been the youngest player on the Pelicans since his rookie year.